Question 25147
{{{D = -5p^2+520p-240}}}


to "solve" this - as a purely theoretical question, we want to know where the curve crosses the x-axis, ie where y is zero. In your question you are using D instead of y, so where is D=0...


{{{0 = -5p^2+520p-240}}}
and re-arranging gives
{{{5p^2 - 520p + 240 = 0}}}
{{{p^2 - 104p + 48 = 0}}}
this does not factorise, so use the quadratic formula.


This produces 2 answers for p, namely p=0.465 and p=103.535.


Now any quadratic is a symmetrical curve so, the maximum lies mid-way between these 2 values... namely at (0.465+103.535)/2 --> p=52.

So, the price at which it sells the maximum number of drills is $52
This corresponds to {{{D=-(52)^2 + 520(52) - 240}}} drills
{{{D = -2704 + 27040 - 240}}} drills
D = 24096 drills


As for a graph... pick a few values of p, put each into the equation as i did and find corresponding values of D then plot them.


jon.